132.

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diagonal of the GLCM, and consequently, this equation will generate higher value of Con. For instance, Con for Figure 5.16a is 0.37, while for Figure 5.16b Con is 3.04.

(3) Inverse Difference Moment (IDM):

(5.42)

This measure will generate higher values for an image containing large homogeneous patches, because such an image generates high values on the main diagonal of the GLCM. It gives lower weight to those p(i, j) that are located away from the main diagonal. For instance, the data shown in Figure 5.16a gives an IDM value of 0.92, while the value of IDM for the image Figure 5.16b is 0.39.

(1) Entropy (Ent):

(5.43)

The Entropy measure outputs a higher value for a homogeneous distribution of p(i, j), and lower otherwise. The value of Ent computed for Figure 5.16a is 1.85, while for Figure 5.16b it is 2.7.

5.4 Multiplicative autoregressive random fields

The multiplicative autoregressive random field (MAR) model was proposed by Frankot and Chellapa (1987). It is used in modelling both the spatial correlation structures and the distribution of grey level values in an image. Although the MAR model was originally used to model radar image data, the parameters of the model have been found to be highly correlated with the spatial distribution of the data and in consequence, can be used as texture descriptors (Schistad et al., 1994).

5.4.1 MAR model: definition

MAR is a natural extension of the Gaussian autoregressive random model with multiplicative behaviour. Let an image x(i, j) be represented by the following white-noise-driven multiplicative system:

(5.44)

N is the neighbourhood set defining model support, v(i, j) is a lognormal

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